Evaluate the following definite integrals: _ -2 ^31 x+7 dx - Vidyadip

Question

Evaluate the following definite integrals:
$\int_{-2}^\limits{3}\frac{1}{\text{x}+7} \text{ dx}$

✓

Answer

We know that $\int\frac{\text{dx}}{\text{x}}=\log\text{x}+\text{C}$
Now,
$\int_{-2}^\limits{3}\frac{1}{\text{x}+7} \text{ dx}$
$=\big[\log(\text{x}+7)\big]^3_{-2}$
$=\big[\log10-\log5]^3_{-2}$
$=\log\frac{10}{5}$ $\Big[\because\log\text{a}-\log\text{b}=\log\frac{\text{a}}{\text{b}}\Big]$
$=\log2$
$\therefore\ \int_{-2}^\limits{3}\frac{1}{\text{x}+7} \text{ dx}=\log2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the integral: $\int\left(4 e^{3 x}+1\right) d x$

In a parliament election, a political party hired a public relations firm to promote its candidates in three ways - telephone, house calls and letters. The cost per contact (in paisa) is given in matrix A as
$\text{A}=\begin{bmatrix}140&\text{Telephone}\\200&\text{House calls}\\150&\text{Letters}\end{bmatrix}$
The number of contacts of each type made in two cities X and Yis given in the matrix B as
$\begin{matrix}\text{Telephone}&\text{House calls}&\text{Letters}\end{matrix}\\\text{B}=\begin{bmatrix}1000&500&5000\\3000&1000&10000\end{bmatrix}\begin{matrix}\text{City X}\\\text{City Y}\end{matrix}$
Find the total amount spent by the party in the two cities.
What should one consider before casting his/ her vote - party's promotional activity of their social activities?

Find the second order derivatives of the function given in Exercise:
$\text{e}^\text{x}\sin5\text{x}$

Evaluate the following integrals:
$\int\limits^1_{-2}\frac{|\text{x}|}{\text{x}}\text{ dx}$

If A is 2×3 matrix and B is a matrix such that A^T B and BA^T both are defined, then what is the order of B?

Find the principal value of the following:
$\cos^{-1}\Big(\sin\frac{4\pi}{3}\Big)$

Let A be a 3 × 3 square matrix, such that A (adj A) = 2I, where I is the identity matrix. Write the value of |adj A|.

Which of the following distributions of a random variable X are the probability distributions?

X:	3	2	1	0	-1
P(X):	0.3	0.2	0.4	0.1	0.05

Write the following function in the simplest form:
$\tan^{-1}\bigg(\frac{\sqrt{1-\cos x}}{\sqrt{1+\cos x}}\bigg), x<{\pi}$

Evaluate $\int\frac{\sin\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$